College Physics

Hugh D. Young

Chapter 24

Geometric Optics - all with Video Answers

Educators

Chapter Questions

Problem 1

$\cdot$ A candle 4.85 $\mathrm{cm}$ tall is 39.2 $\mathrm{cm}$ to the left of a plane mirror. Where is the image formed by the mirror, and what is the height of this image?

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Katie Mcalpine

Numerade Educator

Problem 2

What is the size of the smallest vertical plane mirror in which a 10 ft tall giraffe standing erect can see her full-length image? (Hint: Locate the image by drawing a number of rays from the giraffe's body that reflect off the mirror and go to her eye. Then eliminate that part of the mirror for which the reflected rays do not reach her eye.)

Farhanul Hasan

Numerade Educator

Problem 3

An object is placed between two plane mirrors arranged at right angles to each other at a distance $d_{1}$ from the surface of one mirror and a distance $d_{2}$ from the surface of the other. (a) How many images are formed? Show the location of the images in a diagram.

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Problem 4

$\bullet$ If you run away from a plane mirror at $2.40 \mathrm{m} / \mathrm{s},$ at wha speed does your image move away from you?

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Numerade Educator

Problem 5

A concave spherical mirror has a radius of curvature of 10.0 $\mathrm{cm} .$ Calculate the location and size of the image formed of an 8.00 -mm-tall object whose distance from the mirror is (a) $15.0 \mathrm{cm},(\mathrm{b}) 10.0 \mathrm{cm},(\mathrm{c}) 2.50 \mathrm{cm},$ and (d) 10.0 $\mathrm{m}$

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Problem 6

$\cdot$ Repeat the previous problem, except use a convex mirror with the same magnitude of focal length.

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Problem 7

$\cdot$ The diameter of Mars is $6 / 94 \mathrm{km},$ and its minimum distance from the earth is $5.58 \times 10^{7} \mathrm{km}$ . (a) When Mars is at this distance, find the diameter of the image of Mars formed by aspherical, concave telescope mirror with a focal length of 1.75 $\mathrm{m} .$ (b) Where is the image located?

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Numerade Educator

Problem 8

$\cdot$ A concave mirror has a radius of curvature of 34.0 $\mathrm{cm}$ . (a) What is its focal length? (b) A ladybug 7.50 $\mathrm{mm}$ tall is located 22.0 $\mathrm{cm}$ from this mirror along the principal axis. Find the location and height of the image of the insect. (c) If the
mirror is immersed in water (of refractive index $1.33 ),$ what is its focal length?

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Numerade Educator

Problem 9

Rearview mirror. A mirror on the passenger side of your car is convex and has a radius of curvature with magnitude 18.0 $\mathrm{cm} .$ (a) Another car is seen in this side mirror and is 13.0 $\mathrm{m}$ behind the mirror. If this car is 1.5 $\mathrm{m}$ tall, what is the height of its image? (b) The mirror has a warning attached that objects viewed in it are closer than they appear. Why is this so?

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Numerade Educator

Problem 10

$\bullet$ Examining your image in a convex mirror whose radius of curvature is $25.0 \mathrm{cm},$ you stand with the tip of your nose 10.0 $\mathrm{cm}$ from the surface of the mirror. (a) Where is the image of your nose located? What is its magnification? (b) Your ear is 10.0 $\mathrm{cm}$
behind the tip of your nose; where is the image of your ear located, and what is its magnification? Do your answers suggest reasons for your strange appearance in a convex mirror?

Farhanul Hasan

Numerade Educator

Problem 11

A $\mathrm{A}$ coin is placed next to the convex side of a thin spherical glass shell having a radius of curvature of 18.0 $\mathrm{cm} .$ An image of the 1.5 -cm-tall coin is formed 6.00 $\mathrm{cm}$ behind the glass shell. Where is the coin located? Determine the size, orientation, and nature (real or virtual) of the image.

Katie Mcalpine

Numerade Educator

Problem 12

$\bullet$ (a) Show that when an object is outside the focal point of a concave mirror, its image is always inverted and real. Is there any limitation on the magnification? (b) Show that when an object is
inside the focal point of a concave mirror, its image is always erect and virtual. Is there any limitation on the magnification?

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Numerade Educator

Problem 13

A spherical, concave shaving mirror has a radius of curva- ture of 32.0 $\mathrm{cm}$ . (a) What is the magnification of a person's face when it is 12.0 $\mathrm{cm}$ to the left of the vertex of the mirror?
(b) Where is the image? Is the image real or virtual? (c) Draw
a principal-ray diagram showing the formation of the image.

Katie Mcalpine

Numerade Educator

Problem 14

An object 0.600 $\mathrm{cm}$ tall is placed 16.5 $\mathrm{cm}$ to the left of the
vertex of a concave spherical mirror having a radius of curvature of 22.0 $\mathrm{cm} .$ (a) Draw a principal-ray diagram showing the formation of the image. (b) Calculate the position, size,
orientation (erect or inverted), and nature (real or virtual) of the image.

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Problem 15

$\cdot$ Repeat the previous problem for the case in which the mirror is convex.

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Problem 16

$\cdot$ The stainless steel rear end of a tanker truck is convex, shiny, and has a radius of curvature of 2.0 $\mathrm{m} .$ You're tailgating the truck, with the front end of your car only 5.0 $\mathrm{m}$
behind it. Making the not very realistic assumption that your car is on the axis of the mirror formed by the tank, (a) determine the position, orientation, magnification, and type (real or virtual) of the image of your car's front end that forms in this mirror; (b) draw a principal-ray diagram of the situation to check your answer.

Farhanul Hasan

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Problem 17

The thin glass shell shown in Figure 24.44 has a spherical shape with a radius of curvature of $12.0 \mathrm{~cm},$ and both of its surfaces
the center of the mirror along the can act as mirrors. A seed 3.30 $\mathrm{mm}$ high is placed $15.0 \mathrm{~cm}$ from
optic axis, as shown in the figure.
(a) Calculate the location and $\Delta$ FIGURE 24.44 height of the image of this seed. Problem 17 .
(b) Suppose now that the shell is reversed. Find the location and height of the seed's image.

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Problem 18

. Dental mirror. A dentist uses a curved mirror to view teeth on the upper side of the mouth. Suppose she wants an erect image with a magnification of 2.00 when the mirror is 1.25 $\mathrm{cm}$ from a tooth. (Treat this problem as though the object and image lie along a straight line.) (a) What kind of mirror (concave or convex) is needed? Use a ray diagram to
decide, without performing any calculations. (b) What must be the focal length and radius of curvature of this mirror? (c) Draw a principal-ray diagram to check your answer in
part (b).

Farhanul Hasan

Numerade Educator

Problem 19

$\cdot$ The left end of a long glass rod 6.00 $\mathrm{cm}$ in diameter has a convex hemispherical surface 3.00 $\mathrm{cm}$ in radius. The refractive index of the glass is $1.60 .$ Determine the position of the image if an object is placed in air on the axis of the rod at the following distances to the left of the vertex of the curved end: (a) infinitely far, (b) $12.0 \mathrm{cm},$ and $(c) 2.00 \mathrm{cm} .$

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Numerade Educator

Problem 20

$\cdot$ The rod of the previous problem is immersed in a liquid. An
object 90.0 $\mathrm{cm}$ from the vertex of the left end of the rod and on
its axis is imaged at a point 1.60 $\mathrm{m}$ inside the rod. What is the
refractive index of the liquid?

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Numerade Educator

Problem 21

$\cdot$ The left end of a long glass rod 8.00 $\mathrm{cm}$ in diameter and with an index of refraction of 1.60 is ground and polished to a convex hemispherical surface with a radius of 4.00 $\mathrm{cm} .$ An object in the form of an arrow 1.50 $\mathrm{mm}$ tall, at right angles to the axis of the rod, is located on the axis 24.0 $\mathrm{cm}$ to the left of the vertex of the convex surface. Find the position and height of the image of the arrow formed by paraxial rays inci- dent on the convex surface. Is the image erect or inverted?

Katie Mcalpine

Numerade Educator

Problem 22

A large aquarium has portholes of thin transparent plastic with a radius of curvature of 1.75 $\mathrm{m}$ and their convex sides fac- ing into the water. A shark hovers in front of a porthole, sizingup the dinner prospects outside the tank. (a) If one of the shark's teeth is exactly 45.0 $\mathrm{cm}$ from the plastic, how far from the plastic does it appear to be to observers outside the tank?You can ignore refraction due to the plastic.) (b) Does the shark appear to be right side up or upside down? (c) If the tooth has an actual length of 5.00 $\mathrm{cm}$ , how long does it appear
to the observers?

Farhanul Hasan

Numerade Educator

Problem 23

A spherical fishbowl. A small tropical fish is at the center of a water-filled spherical fishbowl $28.0 \mathrm{~cm}$ in diameter.
(a) Find the apparent position and magnification of the fish to an observer outside the bowl. The effect of the thin walls of the bowl may be ignored. (b) A friend advised the owner of the bowl to keep it out of direct sunlight to avoid blinding the fish, which might swim into the focal point of the parallel rays from the sun. Is the focal point actually within the bowl?

Katie Mcalpine

Numerade Educator

Problem 24

Focus of the eye. The cornea of the eye has a radius of curvature of approximately $0.50 \mathrm{cm},$ and the aqueous humor bbehind it has an index of refraction of $1.35 .$ The thickness of
the cornea itself is small enough that we shall neglect it. The depth of a typical human eye is around 25 5 $\mathrm{mm}$ . (a) What would have to be the radius of curvature of the cornea so that it alone would focus the image of a distant mountain on the retina, which is at the back of the eye opposite the cornea? (b) If the cornea focused the mountain correctly on the retina as described in part $(a),$ would it also focus the text from a computer screen on the retina if that screen were 25 $\mathrm{cm}$ in front of the eye? If not, where would it focus that text, in front of or
behind the retina? (c) Given that the cornea has a radius of curvature of about $5.0 \mathrm{mm},$ where does it actually focus the mountain? Is this in front of or behind the retina? Does this
help you see why the eye needs help from a lens to complete
the task of focusing?

Farhanul Hasan

Numerade Educator

Problem 25

A speck of dirt is embedded 3.50 $\mathrm{cm}$ below the surface of a
sheet of ice having a refractive index of $1.309 .$ What is the
apparent depth of the speck, when viewed from directly above?

Katie Mcalpine

Numerade Educator

Problem 26

$\cdot$ A skin diver is 2.0 $\mathrm{m}$ below the surface of a lake. A bird flies overhead 7.0 $\mathrm{m}$ above the surface of the lake. When the bird is directly overhead, how far above the diver does it appear to be?

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Problem 27

$\bullet \mathrm{A}$ zoo aquarium has transparent walls, so that spectators on both sides of it can watch the fish. The aquarium is 5.50 $\mathrm{m}$ across, and the spectators on both sides of it are standing 1.20 $\mathrm{m}$ from the wall. How far away do spectators on one side of the
aquarium appear to those on the other side? (Ignore any refraction in the walls of the aquarium.)

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Numerade Educator

Problem 28

$\cdot$ To a person swimming 0.80 $\mathrm{m}$ beneath the surface of the water in a swimming pool, the diving board directly overhead appears to be a height of 5.20 $\mathrm{m}$ above the swimmer. What is the actual height of the diving board above the surface of the
water?

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Numerade Educator

Problem 29

$\cdot$ A converging lens with a focal length of 7.00 $\mathrm{cm}$ forms an
image of a 4.00 -mm-tall real object that is to the left of the lens. The image is 1.30 $\mathrm{cm}$ tall and erect. Where are the object and image located? Is the image real or virtual?

Katie Mcalpine

Numerade Educator

Problem 30

A converging lens with a focal length of 90.0 $\mathrm{cm}$ forms an image of a 3.20 -cm-tall real object that is to the left of the lens. The image is 4.50 $\mathrm{cm}$ tall and inverted. Where are the object and image located in relation to the lens? Is the image real or virtual?

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Numerade Educator

Problem 31

$\cdot$ You are standing in front of a lens that projects an image of you onto a wall 1.80 $\mathrm{m}$ on the other side of the lens. This image is three times your height. (a) How far are you from the lens? (b) Is your image erect or inverted? (c) What is the focal length of the lens? Is the lens converging or diverging?

Katie Mcalpine

Numerade Educator

Problem 32

$\bullet$ Figure 24.45 shows an object and its image formed by a
thin lens. (a) What is the focal length of the lens and what type
of lens (converging or diverging) is it? (b) What is the height
of the image? Is it real or virtual?

Farhanul Hasan

Numerade Educator

Problem 33

$\bullet$ Figure 24.46 shows an object and its image formed by a
thin lens. (a) What is the focal length of the lens and what type
of lens (converging or diverging) is it? (b) What is the height
of the image? Is it real or virtual?

Katie Mcalpine

Numerade Educator

Problem 34

.. Figure 24.47 shows an object and its image formed by a
thin lens. (a) What is the focal length of the lens and what type
of lens (converging or diverging) is it? (b) What is the height
of the image? Is it real or virtual?

Farhanul Hasan

Numerade Educator

Problem 35

$\cdot$ The two surfaces of a plastic converging lens have equal radii of curvature of $22.0 \mathrm{cm},$ and the lens has a focal length of 20.0 $\mathrm{cm} .$ Calculate the index of refraction
of the plastic.

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Numerade Educator

Problem 36

$\cdot$ The front, convex, surface of a lens made for eyeglasses has a radius of curvature of $11.8 \mathrm{cm},$ and the back, concave, surface has a radius of curvature of 6.80 $\mathrm{cm} .$ The index of refraction of the plastic lens material is 1.67 . Calculate the local length of the lens.

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Numerade Educator

Problem 37

For each of the thin lenses $\left(L_{1}\right.$ and $\left.L_{2}\right)$ shown in Figure 24.48 , the index of refraction of the lens' glass is $1.50,$ and the object is to the left of the lens. The radii of curvature indicated are just the magnitudes. Calculate the focal length of each lens.

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Problem 38

$\cdot$ For each thin lens shown in Figure $24.49,$ calculate the loca-
tion of the image of an object that is 18.0 $\mathrm{cm}$ to the left of the
lens. The lens material has a refractive index of $1.50,$ and the
radii of curvature shown are only the magnitudes.

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Numerade Educator

Problem 39

$\cdot$ The lens of the eye. The crystalline lens of the human eye is a double-convex lens made of material having an index of refraction of 1.44 (although this varies). Its focal length in air
is about 8.0 $\mathrm{mm}$ , which also varies. We shall assume that the radii of curvature of its two surfaces have the same magnitude. (a) Find the radii of curvature of this lens. (b) If an object
16 $\mathrm{cm}$ tall is placed 30.0 $\mathrm{cm}$ from the eye lens, where would
the lens focus it and how tall would the image be? Is thisimage real or virtual? Is it erect or inverted? (Note: The results.obtained here are not strictly accurate, because the lens is
embedded in fluids having refractive indexes different from that of air.)

Katie Mcalpine

Numerade Educator

Problem 40

The cornea as a simple lens. The cornea behaves as a thin lens of focal length approximately $1.8 \mathrm{cm},$ although this varies a bit. The material of which it is made has an index of
refraction of 1.38 and its front surface is convex, with a radius of curvature of 5.0 $\mathrm{mm}$ . (a) If this focal length is in air, what is the radius of curvature of the back side of the
cornea? (b) The closest distance at which a typical person can focus on an object (called the near point) is about 25 $\mathrm{cm}$ ,although this varies considerably with age. Where would the
cornea focus the image of an 8.0 -mm-tall object at the near point? (c) What is the height of the image in part (b)? Is this image real or virtual? Is it erect or inverted? (Note: The results obtained here are not strictly accurate, because, on one side, the cornea has a fluid with a refractive index different from that of air.)

Farhanul Hasan

Numerade Educator

Problem 41

$\cdot$ An insect 3.75 $\mathrm{mm}$ tall is placed 22.5 $\mathrm{cm}$ to the left of a thin
planoconvex lens. The left surface of this lens is flat, the right surface has a radius of curvature of magnitude $13.0 \mathrm{cm},$ and the index of refraction of the lens material is 1.70 . (a) Calcu-
late the location and size of the image this lens forms of the insect. Is it real or virtual? erect or inverted? (b) Repeat part (a) if the lens is reversed.

Katie Mcalpine

Numerade Educator

Problem 42

A double-convex thin lens has surfaces with equal radii of
curvature of magnitude 2.50 $\mathrm{cm} .$ Looking through this lens,
you observe that it forms an image of a very distant tree, at a
distance of 1.87 $\mathrm{cm}$ from the lens. What is the index of refrac-
tion of the lens?

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Numerade Educator

Problem 43

(. A converging meniscus lens (see Fig. 24.31$)$ with a refrac-
tive index of 1.52 has spherical surfaces whose radii are 7.00
$\mathrm{cm}$ and 4.00 $\mathrm{cm} .$ What is the position of the image if an
object is placed 24.0 $\mathrm{cm}$ to the left of the lens? What is the
magnification?

Katie Mcalpine

Numerade Educator

Problem 44

$\bullet$ A converging lens with a focal length of 12.0 $\mathrm{cm}$ forms
virtual image 8.00 $\mathrm{mm}$ tall, 17.0 $\mathrm{cm}$ to the right of the lens
Determine the position and size of the object. Is the image
erect or inverted? Are the object and image on the same side o
opposite sides of the lens?

Farhanul Hasan

Numerade Educator

Problem 45

Focus of the eye. The cornea of the eye has a radius of curvature of approximately $0.50 \mathrm{~cm},$ and the aqueous humor behind it has an index of refraction of $1.35 .$ The thickness of the cornea itself is small enough that we shall neglect it. The depth of a typical human eye is around $25 \mathrm{~mm}$. (a) What would have to be the radius of curvature of the cornea so that it alone would focus the image of a distant mountain on the retina, which is at the back of the eye opposite the cornea? (b) If the cornea focused the mountain correctly on the retina as described in part (a), would it also focus the text from a computer screen on the retina if that screen were $25 \mathrm{~cm}$ in front of the eye? If not, where would it focus that text, in front of or behind the retina? (c) Given that the cornea has a radius of curvature of about $5.0 \mathrm{~mm},$ where does it actually focus the mountain? Is this in front of or behind the retina? Does this
help you see why the eye needs help from a lens to complete the task of focusing?

Katie Mcalpine

Numerade Educator

Problem 46

$\cdot($ a) You want to use a lens with a focal length of 35.0 $\mathrm{cm}$ to produce a real image of an object, with the image twice as long as the object itself. What kind of lens do you need, and where
should the object be placed? (b) Suppose you want a virtual image of the same object, with the same magnification - what kind of lens do you need, and where should the object be placed?

Farhanul Hasan

Numerade Educator

Problem 47

.. Combination of lenses, II. Two thin lenses with a focal length of magnitude $12.0 \mathrm{cm},$ the first diverging and the second converging, are located 9.00 $\mathrm{cm}$ apart. An object 2.50 $\mathrm{mm}$ tall is placed 20.0 $\mathrm{cm}$ to the left of the first (diverging) lens.(a) How far from this first lens is the final image formed? (b) Is the final image real or virtual? (c) What is the height of the final image? Is it erect or inverted? (Hint: See Problem 45.)

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Numerade Educator

Problem 48

A lens forms a real image, which is 214 $\mathrm{cm}$ away from the
object and 1$\%$ times its length. What kind of lens is this, and
what is its focal length?

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Numerade Educator

Problem 49

A converging lens has a focal length of 14.0 $\mathrm{cm} .$ For each of two objects located to the left of the lens, one at a distance of 18.0 $\mathrm{cm}$ and the other at a distance of $7.00 \mathrm{cm},$ determine (a) the image position, (b) the magnification, (c) whether the image is real or virtual, and (d) whether the image is erect or inverted. Draw a principal-ray diagram in each case.

Katie Mcalpine

Numerade Educator

Problem 50

A converging lens forms an image of an $8.00-$ mm-tall real object. The image is 12.0 $\mathrm{cm}$ to the left of the lens, 3.40 $\mathrm{cm}$ tall, and erect. (a) What is the focal length of the lens?
(b) Where is the object located? (c) Draw a principal-ray dia- gram for this situation.

Farhanul Hasan

Numerade Educator

Problem 51

A diverging lens with a focal length of $-48.0 \mathrm{cm}$ forms a virtual image 8.00 $\mathrm{mm}$ tall, 17.0 $\mathrm{cm}$ to the right of the lens. (a) Determine the position and size of the object. Is the image erect or inverted? Are the object and image on the same side or
opposite sides of the lens? (b) Draw a principal-ray diagram for this situation.

Katie Mcalpine

Numerade Educator

Problem 52

$\cdot$ When an object is 16.0 $\mathrm{cm}$ from a lens, an image is formed 12.0 $\mathrm{cm}$ from the lens on the same side as the object. (a) What is the focal length of the lens? Is the lens converging or diverging? (b) If the object is 8.50 $\mathrm{mm}$ tall, how tall is the image? Is
it erect or inverted? (c) Draw a principal-ray diagram.

Farhanul Hasan

Numerade Educator

Problem 53

. Figure 24.50 shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Fach square is 2.0 $\mathrm{cm}$ along the horizontal direction, but the vertical direction
is not to the same scale. Use information from the diagram to answer the following questions: (a) Using only the ray shown, decide what type of lens (converging or diverging) this is. (b) What is the focal length of the lens? (c) Locate the image by drawing the other two principal rays. (d) Calculate where
the image should be, and compare this result with the graphical solution in part (c).

Katie Mcalpine

Numerade Educator

Problem 54

$\bullet$ Figure 24.51 shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Each square is 2.0 $\mathrm{cm}$ along the horizontal direction, but the vertical direction is not to the same scale. Use information from the dia- gram to answer the following questions: (a) Using only the ray shown, decide what type of lens (converging or diverging) this is. (b) What is the focal
length of the lens? (c) Locate the image by drawing the other two principal rays. (d) Calculate where the image should be, and compare this result with the graphical solution in part (c).

Farhanul Hasan

Numerade Educator

Problem 55

Figure 24.52 shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Fach square is 2.0 $\mathrm{cm}$ along the horizontal direction, but the vertical direction is not to the same scale. Use information from the diagram to answer the following questions: (a) Using only the ray shown, decide what type of lens (converging or diverging) this is. (b) What is the focal length of the lens? (c) Locate the image by drawing the other two principal rays. (d) Calculate where the image should be, and compare this result with the graphi- cal solution in part (c).

Katie Mcalpine

Numerade Educator

Problem 56

$\bullet$ Figure 24.53 shows a small plant near a thin lens. The ray shown is one of the principal rays for the lens. Each syuare is 2.0 $\mathrm{cm}$ along the horizontal direction, but
the vertical direction is not to the same scale. Use infor- mation from the diagram to answer the following questions: (a) Using only the ray shown,
decide what type of lens (converging or diverging) this is.
(b) What is the focal length of the lens? (c) Locate the image
by drawing the other two principal rays. (d) Calculate where
the image should be, and compare this result with the graphi-
cal solution in part (c).

Farhanul Hasan

Numerade Educator

Problem 57

\bullet A layer of benzene $(n=1.50) 2.60 \mathrm{cm}$ deep floats on
water $(n=1.33)$ that is 6.50 $\mathrm{cm}$ deep. What is the apparent
distance from the upper benzene surface to the bottom of the
water laver when it is viewed at normal incidence?

Katie Mcalpine

Numerade Educator

Problem 58

.. Where must you place an object in front of a concave mir-
ror with radius $R$ so that the image is erect and 2$\frac{1}{2}$ times the
size of the object? Where is the image?

Farhanul Hasan

Numerade Educator

Problem 59

A luminous object is 4.00 $\mathrm{m}$ from a wall. You are to use a
concave mirror to project an image of the object on the wall,
with the image 2.25 times the size of the object. How far
should the mirror be from the wall? What should its radius of
curvature be?

Katie Mcalpine

Numerade Educator

Problem 60

A concave mirror is to form an image of the filament of a headlight lamp on a screen 8.00 m from the mirror. The filament is 6.00 mm tall, and the image is to be 36.0 $\mathrm{cm}$ tall. (a) How far in front of the vertex of the mirror should the filament be placed? (b) To what radius of curvature should you
grind the mirror?

Farhanul Hasan

Numerade Educator

Problem 61

" A plastic lens $(n=1.67)$ has one convex surface of radius 12.2 $\mathrm{cm}$ and one concave surface of radius 15.4 $\mathrm{cm} .$ If an object is placed 35.0 $\mathrm{cm}$ from the lens, (a) where is the image located and (b) what is its magnification?

Katie Mcalpine

Numerade Educator

Problem 62

$\cdot$ A 3.80 -mm-tall object is 24.0 $\mathrm{cm}$ from the center of a sil-
vered spherical glass Christmas tree ornament 6.00 $\mathrm{cm}$ in
diameter, What are the position and height of its image?

Farhanul Hasan

Numerade Educator

Problem 63

A A lensmaker wants to make a magnifying glass from glass
with $n=1.55$ and with a focal length of 20.0 $\mathrm{cm} .$ If the two
surfaces of the lens are to have equal radii, what should that
radius be?

Katie Mcalpine

Numerade Educator

Problem 64

An object is placed 18.0 $\mathrm{cm}$ from a screen. (a) At what two
points between object and screen may a converging lens with a
3.00 $\mathrm{cm}$ focal length be placed to obtain an image on the
screen? (b) What is the magnification of the image for each
position of the lens?

Farhanul Hasan

Numerade Educator

Problem 65

As shown in Figure $24.54,$ a candle is at the center of curvature of a concave mirror whose focal length is 10.0 $\mathrm{cm}$ . The converging lens has a focal length of 32.0 $\mathrm{cm}$ and is 85.0 $\mathrm{cm}$ to the right of the candle. The candle is viewed through the lens from the right. The lens forms two images of the candle. The first is formed by light passing directly through the lens. The
second image is formed from the light that goes from the candle to the mirror, is reflected, and then passes through the lens.(a) For each of these two images, draw a principal-ray diagram that locates the image. (b) For each image, answer the following questions: (i) Where is the image? (ii) Is the image real or virtual? (ii) Is the image erect or inverted with respect to the original object?

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Problem 66

In the text, Equations $(24.4)$ and $(24.7)$ were derived for
the case of a concave mirror. Give a similar derivation for a
convex mirror, and show that the same equations result if you
use the sign convention established in the text.

Farhanul Hasan

Numerade Educator

Problem 67

$\bullet$ A lens in a liquid. A lens obeys Snell's law, bending light
rays at each surface an amount determined by the index of
refraction of the lens and the index of the medium in which the
lens is located. (a) Equation $(24.20)$ assumes that the lens is
surrounded by air. Consider instead a thin lens immersed in a

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Problem 68

Refraction of liquids. The focal length of a mirror can be determined entirely from the shape of the mirror. In contrast, to determine the focal length of a lens we must know both the shape of the lens and its index of refraction - and the index of refraction of the surrounding medium. For instance, when a thin lens is immersed in a liquid we must modify the thin-lens equation to take into account the refractive properties of the surrounding liquid: $\frac{1}{f}=\left(\frac{n}{n_{\mathrm{liq}}}-1\right)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$
where $n_{1 \mathrm{in}}$ is the index of refraction of the liquid and $n$ is the index
of refraction of the glass.
If you place a glass lens $(n=1.5),$ which has a focal length of
0.5 meters in air, into a tank of water $(n=1.33),$ what will happen to its focal length?
A. Nothing will happen.
B. The focal length of the lens will be reduced.
C. The focal length of the lens will be increased.
D. There is not enough information to answer the question.

Farhanul Hasan

Numerade Educator

Problem 69

If you place a concave glass lens into a tank of a liquid that has
an index of refraction that is greater than that of the lens, what
will happen? A. The lens will no longer be able to create any images.
B. The focal length of the lens will become longer.
C. The focal length of the lens will become shorter.
D. The lens will become a converoing lens

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Problem 70

If you place a concave mirror with a focal length of 1 $\mathrm{m}$ into a
liquid that has an index of refraction of $3,$ what will happen?
A. The mirror will no longer be able to focus light.
B. The focal length of the mirror will decrease.
C. The focal length of the mirror will increase.
D. Nothing will happen.

Farhanul Hasan

Numerade Educator